Many real world learning problems are best characterized by an interaction of multiple independent causes or factors. Discovering suchcausal structure from the data is the focus of this paper. Based on Zemel and Hinton's cooperative vector quantizer (CVQ) architecture, an unsupervised learning algorithm is derived from the Expectation-Maximization (EM) framework. Due to the combinatorial natureof the data generation process, the exact E-step is computationally intractable. Two alternative methods for computing theE-step are proposed: Gibbs sampling and mean-field approximation, and some promising empirical results are presented.

In this paper, we derive classifiers which are winner-take-all (WTA) approximations to a Bayes classifier with Gaussian mixtures for class conditional densities. The derived classifiers include clustering based algorithms like LVQ and k-Means. We propose a constrained rank Gaussian mixtures model and derive a WTA algorithm for it. Our experiments with two speech classification tasks indicate that the constrained rank model and the WTA approximations improve the performance over the unconstrained models. 1 Introduction A classifier assigns vectors from Rn (n dimensional feature space) to one of K classes, partitioning the feature space into a set of K disjoint regions. A Bayesian classifier builds the partition based on a model of the class conditional probability densities of the inputs (the partition is optimal for the given model).

Diagnosis of human disease or machine fault is a missing data problem since many variables are initially unknown. Additional information needs to be obtained. The j oint probability distribution of the data can be used to solve this problem. We model this with mixture models whose parameters are estimated by the EM algorithm. This gives the benefit that missing data in the database itself can also be handled correctly. The request for new information to refine the diagnosis is performed using the maximum utility principle. Since the system is based on learning it is domain independent and less labor intensive than expert systems or probabilistic networks. An example using a heart disease database is presented.

Multi-class classification problems can be efficiently solved by partitioning the original problem into sub-problems involving only two classes: for each pair of classes, a (potentially small) neural network is trained using only the data of these two classes. We show how to combine the outputs of the two-class neural networks in order to obtain posterior probabilities for the class decisions. The resulting probabilistic pairwise classifier is part of a handwriting recognition system which is currently applied to check reading. We present results on real world data bases and show that, from a practical point of view, these results compare favorably to other neural network approaches.

In practical situations, experts may visually examine the images and provide a subjective noisy estimate of the truth. Calibrating the reliability and bias of expert labellers is a nontrivial problem. In this paper we discuss some of our recent work on this topic in the context of detecting small volcanoes in Magellan SAR images of Venus. Empirical results (using the Expectation-Maximization procedure) suggest that accounting for subjective noise can be quite significant interms of quantifying both human and algorithm detection performance.

If data collection is costly, there is much to be gained by actively selecting particularlyinformative data points in a sequential way. In a Bayesian decision-theoretic framework we develop a query selection criterionwhich explicitly takes into account the intended use of the model predictions. By Markov Chain Monte Carlo methods the necessary quantities can be approximated to a desired precision. Asthe number of data points grows, the model complexity is modified by a Bayesian model selection strategy. The properties oftwo versions of the criterion ate demonstrated in numerical experiments.

We present a deterministic annealing variant of the EM algorithm maximum likelihood parameter estimation problems. In ourfor approach, the EM process is reformulated as the problem of minimizing the thermodynamic free energy by using the principle of maximum entropy and statistical mechanics analogy. Unlike simulated deterministicallyannealing approaches, this minimization is performed. Moreover, the derived algorithm, unlike the conventional better estimates free of the initialEM algorithm, can obtain parameter values.

Signal processing and classification algorithms often have limited applicability resulting from an inaccurate model of the signal's underlying structure. We present here an efficient, Bayesian algorithm for modeling a signal composed of the superposition of brief, Poisson-distributed functions. This methodology is applied to the specific problem of modeling and classifying extracellular neural waveforms which are composed of a superposition of an unknown number of action potentials CAPs). Previous approaches have had limited success due largely to the problems of determining the spike shapes, deciding how many are shapes distinct, and decomposing overlapping APs. A Bayesian solution to each of these problems is obtained by inferring a probabilistic model of the waveform. This approach quantifies the uncertainty of the form and number of the inferred AP shapes and is used to obtain an efficient method for decomposing complex overlaps. This algorithm can extract many times more information than previous methods and facilitates the extracellular investigation of neuronal classes and of interactions within neuronal circuits.

MacKay's Bayesian framework for backpropagation is conceptually appealing as well as practical. It automatically adjusts the weight decay parameters during training, and computes the evidence for each trained network. The evidence is proportional to our belief in the model. In this paper, the framework is extended to pruned nets, leading to an Ockham Factor for "tuning the architecture to the data". A committee of networks, selected by their high evidence, is a natural Bayesian construction.

The past several years have seen a tremendous growth in the complexity of the recognition, estimation and control tasks expected of neural networks. In solving these tasks, one is faced with a large variety of learning algorithms and a vast selection of possible network architectures. After all the training, how does one know which is the best network? This decision is further complicated by the fact that standard techniques can be severely limited by problems such as over-fitting, data sparsity and local optima. The usual solution to these problems is a winner-take-all cross-validatory model selection.